When you're getting a "name lookup timeout", it means your server is unable to find Facebook's server. That can be a mis-configuration issue on the server or a firewall or other security measure which are specifically blocking outgoing requests to Facebook and possibly other servers.
There's nothing we can do on our end to fix that type of problem. I'd recommend contacting your hosting provider to understand if there have been changes made and have them test to see if your server can access:
graph.facebook.com
There are many other URLs in addition to that one that need to be accessible, but that's a good starting point.
I hope that helps,
Alex